PRESENTED BY : PRIYANSHU

KUMARCLASS : 9TH A

Motionchapter: 8

Chapter : 8 ….Motion

Important notes to remember :

A common characteristics of all the moving bodies is that they change their

position with time.A body is said to be in motion (or moving) when its position changes

continuously with respect to a stationary object taken as reference point.

if a body moves fairly fast, then its movement (or motion) can be observed easily. But if a body moves very slowly then its become difficult to observe its

movement immediately.

the distance travelled by a body is the actual length of the path covered by a moving body irrespective to the direction in which the body travels.

When a body moves from one point to another, the distance travels refers to the actual length of the indirect path whereas displacement refers to the straight line path between the initial and final position .

when a body moves from one position to another, the shortest (straight line) distance between the initial and position and final position of the body, alongwith direction, is known as its displacement.

the distance travelled has only magnitude whereas displacement has magnitude as well as direction.

The quantities like distance and displacement etc are known as physical quantities. The magnitude of a physical quantity means size of the physical quantity. A physical quantity having only magnitude is known as scalar quantity. A scalar quantity has no direction . On the other hand a physical quantity having magnitude as well as directions known as vector quantity.

1 } distance is a scalar quantity (because it has magnitude only , it has no specified direction)

2} displacement is a vector quantity (because it has magnitude as well as a direction)

3 } the distance travelled by a moving body cannot be zero but the final displacement of a moving body can be zero.

if we take a round trip and reach back at the starting point then, though we have travelled some distance but our final displacement will be zero. This is because the straight line distance between the initial and final positions will be zero.

a body has a uniform motion if it travels equal distances in equal intervals of time, no matter how small these time intervals may be.

a body has a non uniform motion if it travels unequal distance I equal intervals of time.

non uniform motion is also known as accelerated motion.

the motion of body can be described by three terms : speed, velocity and acceleration.

the formula of speed can be written as : speed = distance travelled/ time taken

the SI unit of speed is metres per second which is written as m/s or ms-1

the speed of a running car at any instant of time is shown by an instrument called speedometer.

the distance travelled by a car is measured by another instrument called odometer.

the average speed of a body is the total distance travelled by the total time taken to cover this distance.

average speed = total distance travelled / total time taken

Velocity of a body is the distance travelled by it per unit time in a given direction .that is : velocity = distance travelled in a given direction / time taken

the SI unit of velocity is the same as that of speed, namely metres per second.

Distance travelled = average speed * time

a body has a uniform velocity if it travels in a specified direction in a straight line and moves over equal distances in equal intervals of time, no matter how small these time intervals may be.

the velocity of a body can be changed in two ways :

1} by changing the speed of the body 2 } by keeping the speed constant but

by changing the direction.

the average speed of a moving body can never be zero but the average velocity of a moving body can be zero.

acceleration of a body Is defined as the rate of change of its velocity with time.

acceleration = change in velocity / time taken for change

Change in velocity = final velocity – initial velocity

the SI unit of acceleration is meters per second per second or metres per second square.

when a body is moving uniform velocity its acceleration will be zero.

a body has a uniform acceleration if it travels in a straight line and its velocity increases by equal amount in equal intervals of time.

a body has a non uniform acceleration if its velocity increases by unequal amounts in equal intervals of time.

if the velocity of a body increases, the acceleration is positive and if the velocity of a body decreases the acceleration is negative.

average velocity= initial velocity +final velocity / 2 negative acceleration is known as retardation. retardation is measured in the way as acceleration,

that is retardation is equal to change in velocity / time taken and has the same units of metres per seconds per seconds .

retardation is actually acceleration with the negative sign.

The distance time graph for body having uniform motion is a straight line.

The distance time graph of a body having non uniform motion is a curved line.

Uniform velocity

Equations of uniformly

accelerated motion :

First equation of motion: v = u+at we will now derive the first equation of motion: acceleration =change in velocity /time taken or acceleration = final velocity – initial velocity/

time taken so, a = v-u / tAt = v-uOr, v = u + atWhere v = final velocity of the bodyU = initial velocity of the bodyA = accelerationAnd, t = time taken

Second equation of motion:• S = ut +1/2 at^2• we will now derive the 2nd equation of motion: average velocity= initial velocity +final velocity/2That is, average velocity= u+v/2Also, distance travelled = average velocity * time so , S = (u+v)* t / 2 From the first equation of motion, v = u + at . Putting this value of v

in equation (1) , we get, s = (u+u+at)*t/2 or, s = (2u + at )*t/ 2 or, s = 2ut+ at^2/ 2 or, s = ut + ½ at^2 where s = distance travelled by the body in time tU = initial velocity of the bodyAnd, a = acceleration

Third equation of motion :

• V^2 = u^2 +2as• we will now derive the third equation of motion from the second equation of motion we have : s = ut + ½ at^2 and from the first equation of motion we have v = u+ atThis can be rearranged and written as : or ,T = v-u/aPutting the value of t in equation 1 , we get, or ,S = u(v-u)/a+1/2a {v-u/a}^2Or, uv-u^2/a + a (v^2+u^2-2uv)/2a^2Or ,S= uv -u^2/ a + v^2 + u^2-2uv/2aOr , s = 2uv – 2u^2 +v^2+u^2-2uv/2aOr , 2as = v^2 – u^2Or , v^2= u^2+2aWhere v= final velocity u = initial velocity a = acceleration and ,s = distance travelled

To solve problems on motion we should remember that:

I. if a body starts from rest, its initial velocity , u = 0

II. if a body comes to rest (it stops), its final velocity , v = 0

III. if a body moves with uniform velocity , its acceleration , a = 0

Graphical representation

of motion

a. the distance- time graph of a moving body at uniform speed is always a straight line.

b. the distance – time graph of a body can be used to calculate the speed of the body.

c. the slope of a distance – time graph indicates speed .

a. the speed of a body is non – uniform, then the graph between distance travelled and time is a curved line (called a parabola).

b. if the distance time graph of a body is curved line, then its speed is non- uniform.

a. if the speed – time graph of a body is a straight line parallel to the time axis, then the speed of the body is constant( or uniform).

a. the speed time graph of a uniformly changing speed ( or uniform motion ) will be straight line .

b. we can find out the value of acceleration from the speed – time graph of a moving body.

c. the slope of a speed- time graph of a moving body gives its acceleration.

d. the distance travelled by a moving body in a given time can also be calculated from its speed- time graph .

a.In a speed – time graph of a body, a straight line sloping downwards indicates uniform retardation.

Speed – time graph when the initial velocity of the body is not zero.

Speed – time graph when speed changes at a non- uniform rate (non-uniform acceleration)